Traditionally, the calibration of safety critical nuclear instrumentation has been performed at each refueling cycle. However, many nuclear plants have moved toward condition-directed rather than time-directed calibration. This condition-directed calibration is accomplished through the use of on-line monitoring which commonly uses an autoassociative predictive modeling architecture to assess instrument channel performance. An autoassociative architecture predicts a group of correct sensor values when supplied with a group of sensor values that is corrupted with process and instrument noise, and could also contain faults such as sensor drift or complete failure.
In the U.S. nuclear power industry, millions of dollars are spent annually on the calibration of instrument chains that are performing within the required specifications. For the past twenty years, several nuclear utilities have investigated methods to monitor the calibration of safety critical process instruments. In 2000, the U.S. Nuclear Regulatory Commission (NRC) issued a safety evaluation report (SER) on an EPRI submitted Topical Report (TR) 104965, “On-Line Monitoring of Instrument Channel Performance”. This SER concluded that the generic concept of on-line monitoring (OLM) for tracking instrument performance as discussed in the topical report is acceptable. However, additional requirements were identified that must be addressed by plant specific license amendments if the calibration frequency of safety-related instrumentation is to be relaxed. Since the applicability of an OLM system is directly related to the ability of an empirical model to correctly predict sensor values when supplied faulty data, methods must be developed to ensure that robust empirical models can be developed.
The autoassociative architecture for predicting correct sensor values has also been adapted for use in equipment fault detection and health monitoring. Accordingly, it is known to provide a nonparametric empirical model such as a kernel regression model or a similarity-based model that generates estimates of sensor values responsive to input of measurements of those sensor values in real-time. The estimates are subtracted from the measured values to provide residuals, which are used to detect deviations indicative of incipient equipment failure. Such approaches are known from, for example, U.S. Pat. No. 4,937,763 to Mott; and in U.S. Pat. No. 5,764,509 to Gross et al. In these approaches, a kernel function incorporating a distance function is used to compare the measured values of the sensors arranged as an observation vector, to a set of reference observations. The kernel function, also called a similarity operator, returns a scalar value indicative of the similarity of the input observation vector to each of the reference observation vectors, and these scalar values are used in generating an estimate observation of the sensor values as an adaptive linear combination of at least some of the reference observations. Kernel regression and similarity-based modeling differ in the details of how the adaptive linear combination is formed; however the kernel function is used in both instances. The scalar value or similarity value of the kernel function typically is designed to range between zero and one, where a value of one indicates the compared vectors are identical, and values approaching zero indicate increasing dissimilarity or distance between the vectors.
One of the drawbacks of the kernel functions in use is susceptibility to outlier inputs, especially when the kernel function is executed on the elements of the compared vectors. In such a case, the kernel function compares individual like elements of the vectors, and generates a scalar comparison outcome for each element, then combines those to form an observation level scalar value. When a particular sensor reading is very different from the sensor reading in a reference observation, the observation-level kernel result can be dominated by the outlier sensor value, resulting in a reduced similarity scalar value for the comparison of the input vector to the reference observation in question than might otherwise be implied by the other sensor readings.